02987nam a22004455i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207100008100223245012100304250001800425264007900443300006300522336002600585337002600611338003600637347002400673490006400697505064000761520064201401650002802043650002302071650002802094650002302122700007502145700007902220710003402299773002602333776003602359776003602395830006402431856004602495978-3-030-59656-9DE-He21320251030111359.0cr nn 008mamaa240122s2024    sz |    s    |||| 0|eng d  a97830305965697 a10.1007/978-3-030-59656-92doi 4aQA370-380 7aPBKJ2bicssc 7aMAT0070002bisacsh 7aPBKJ2thema1 aChristopher, Colin.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aLimit Cycles of Differential Equationsh[electronic resource] /cby Colin Christopher, Chengzhi Li, Joan Torregrosa.  a2nd ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Birkhäuser,c2024.  aIX, 238 p. 21 illus., 5 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aAdvanced Courses in Mathematics - CRM Barcelona,x2297-03120 aPart I: Around the Center-Focus Problem -- 1 Centers and Limit Cycles -- 2 Darboux Integrability -- 3 Liouvillian Integrability -- 4 Symmetry -- 5 Cherkas’ Systems -- 6 Monodromy -- 7 The Tangential Center-Focus Problem -- 8 Monodromy of Hyperelliptic Abelian Integrals -- 9 Holonomy and the Lotka-Volterra System -- 10 Other Approaches -- Part II: Abelian Integrals and Applications to the Weak Hilbert’s 16th Problem -- 1 Hilbert’s 16th Problem and Its Weak Form -- 2 Abelian Integrals and Limit Cycles -- 3 Estimate of the Number of Zeros of Abelian Integrals -- 4 A Unified Proof of the Weak Hilbert’s 16th Problem for n=2.  aThis textbook contains the lecture series originally delivered at the "Advanced Course on Limit Cycles of Differential Equations" in the Centre de Recerca Matemàtica Barcelona in 2006. The topics covered are the center-focus problem for polynomial vector fields, and the application of Abelian integrals to limit cycle bifurcations. Both topics are related to Hilbert's sixteenth problem. In particular, the book will be of interest to students and researchers working in the qualitative theory of dynamical systems. This second edition provides updates, further clarifications and remarks, and includes an expanded list of references. 0aDifferential equations. 0aDynamical systems.14aDifferential Equations.24aDynamical Systems.1 aLi, Chengzhi.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aTorregrosa, Joan.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303059655208iPrinted edition:z9783030596576 0aAdvanced Courses in Mathematics - CRM Barcelona,x2297-031240uhttps://doi.org/10.1007/978-3-030-59656-9